Limit theorems for weighted nonlinear transformations of Gaussian stationary processes with singular spectra

Ivanov, Alexander V., Leonenko, Nikolai N. ORCID: https://orcid.org/0000-0003-1932-4091, Ruiz-Medina, María D. and Savich, Irina N. 2013. Limit theorems for weighted nonlinear transformations of Gaussian stationary processes with singular spectra. The Annals of Probability 41 (2) , pp. 1088-1114. 10.1214/12-AOP775

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Abstract

The limit Gaussian distribution of multivariate weighted functionals of nonlinear transformations of Gaussian stationary processes, having multiple singular spectra, is derived, under very general conditions on the weight function. This paper is motivated by its potential applications in nonlinear regression, and asymptotic inference on nonlinear functionals of Gaussian stationary processes with singular spectra.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Subjects:	Q Science > QA Mathematics
Uncontrolled Keywords:	Central limit theorem; isonormal processes; long-range dependence; multiple singular spectra; nonlinear transformations of random processes; Wiener chaos
Publisher:	Institute of Mathematical Statistics
ISSN:	0091-1798
Last Modified:	21 May 2023 11:37
URI:	https://orca.cardiff.ac.uk/id/eprint/45210

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